General N-solitons and their dynamics in several nonlocal nonlinear Schrödinger equations

Publication date: Available online 20 November 2018Source: Physics Letters AAuthor(s): Jianke YangAbstractGeneral N-solitons in three recently-proposed nonlocal nonlinear Schrödinger equations are presented. These nonlocal equations include the reverse-space, reverse-time, and reverse-space–time nonlinear Schrödinger equations, which are nonlocal reductions of the Ablowitz–Kaup–Newell–Segur (AKNS) hierarchy. It is shown that general N-solitons in these different equations can be derived from the same Riemann–Hilbert solutions of the AKNS hierarchy, except that symmetry relations on the scattering data are different for these equations. This Riemann–Hilbert framework allows us to identify new types of solitons with novel eigenvalue configurations in the spectral plane. Dynamics of N-solitons in these equations is also explored. In all the three nonlocal equations, their solutions often collapse repeatedly, but can remain bounded or nonsingular for wide ranges of soliton parameters as well. In addition, it is found that multi-solitons can behave very differently from fundamental solitons and may not correspond to a nonlinear superposition of fundamental solitons.

Source: Physics Letters A - November 21, 2018 Category: Physics Source Type: research